Relaxation rates of Yb$\sp{3+}$ ions incorporated in low concentrations into a host silicate glass have been measured using a pulse saturation/recovery technique at 9.5 GHz over the temperature range 1.5-7.0 K. Compared with similar measurements made on crystalline material, the temperature dependence of the recovery rates for the two-phonon Raman process is anomalously weak (T$\sp6$ instead of T$\sp9$). This anomaly suggests the need to modify the Debye density of states. Fractal models have been suggested for the thermal properties of glasses and for similarly anomalous spin relaxation behavior in proteins. An alternate model is proposed here that is supported by other measurements of low temperature thermal transport properties in glasses. The relaxation rates are interpreted in terms of a "thermally effective" density of states consisting of only low frequency extended vibrational modes. This is smaller than the total density of vibrational modes (extended and localized) measured, for example, by neutron scattering. An estimate for the localization frequency or crossover frequency between these two regimes can be extracted from fits to the lowest concentration data.